Internal problem ID [14504]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.2, page 147
Problem number: 31.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }-y^{\prime }-y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 30
dsolve([diff(y(t),t$2)-diff(y(t),t)-y(t)=0,y(0) = 0, D(y)(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = -\frac {\left (-{\mathrm e}^{\frac {\left (\sqrt {5}+1\right ) t}{2}}+{\mathrm e}^{-\frac {\left (\sqrt {5}-1\right ) t}{2}}\right ) \sqrt {5}}{5} \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 38
DSolve[{y''[t]-y'[t]-y[t]==0,{y[0]==0,y'[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {e^{\frac {1}{2} \left (t-\sqrt {5} t\right )} \left (e^{\sqrt {5} t}-1\right )}{\sqrt {5}} \]